In this paper, we analyze the importance of curvature term structure movements on forecasts of interest rate means. An extension of the exponential three-factor Diebold and Li (2006) model is proposed, where a fourth factor captures a second type of curvature. The new factor increases model ability to generate more volatile and non-linear yield curves, leading to a significant improvement of forecasting ability, in special for short-term maturities. A forecasting experiment adopting Brazilian term structure data on Interbank Deposits (IDs) generates statistically significant lower bias and Root Mean Square Errors (RMSE) for the double curvature model, for most examined maturities, under three different forecasting horizons. Consistent with recent empirical analysis of bond risk premium, when a second curvature is included, despite explaining only a small portion of interest rate variability, it changes the structure of model risk premium leading to better predictions of bond excess returns.

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